1) Field of the Invention
The present invention relates to an observation optical system and a photographing optical system and an apparatus using the same.
2) Description of Related Art
In recent years, development has been energetically made for image display apparatuses, specifically for those to be held on the head or face of individuals for entertaining them with a large image. Also, in accordance with recent popularization of portable telephone and portable intelligent terminal, requirements for large view of graphics or text data on these apparatuses have grown.
As an optical system applicable to such apparatuses, each of FIG. 7(a) of Japanese Patent Application Preliminary Publication (KOKAI) No. 7-140414 and Japanese Patent Application Preliminary Publication (KOKAI) No. 9-171151 proposes an optical system in which a half mirror as a tilted mirror for splitting a path is disposed in a prism optical system that includes a concave mirror with a small amount of decentering.
Also, FIG. 9 of U.S. Pat. No. 5,093,567 proposes an optical system in which a first prism including a triangular prism is disposed on the eye side and in which a second prism is disposed at a minute air space away therefrom. Also, each of FIG. 3 of Japanese Patent Application Preliminary Publication (KOKAI) No. 2000-241751 and FIG. 3 of Japanese Patent Application Preliminary Publication (KOKAI) No. 2000-180787 proposes an optical system in which a first prism having a convex lens action is disposed on the eye side and in which a second prism is disposed at a minute air space away therefrom. These optical systems bend the path of light without loss of amount of light by utilizing total reflection phenomenon caused by difference in refractive index between glass and air at the minute air space between the prisms.
Also, U.S. Pat. No. 4,874,214 proposes an observation optical system having hologram elements. This observation optical system uses the hologram elements at the plane surface (2) and the spherical surface (3).
However, in the optical system as disclosed in FIG. 7(a) of KOKAI No.7-140414 or in KOKAI No. 9-171151, since the tilted mirror disposed in the prism optical system for splitting the path is constructed of a half mirror, amount of light from the image display element is attenuated to xc2xc via twice transmission through the half mirror, to cause dark view of the displayed image. In order to obviate this result, it is necessary to use a bright illumination source, which consumes more power, for illumination of the image display element. If conditions regarding available power consumption, performance of the light source device etc. do not allow a light source to be made bright, observation of the displayed image under bright sunlight could not be made.
Also, in the observation optical system as disclosed in FIG. 9 of U.S. Pat. No. 5,093,567, in FIG. 3 of KOKAI No. 2000-2141751 or in FIG. 3 of KOKAI No. 2000-7180787, since a minute air space is provided between two prisms, alignment of optical axes of these two prisms with each other is required in setting these prisms in place while keeping the air space between, to raise the cost for assembling. Also, impact or vibration applied to an apparatus including such an observation optical system is likely to disorder the alignment of the optical axes.
The optical system proposed in U.S. Pat. No. 4,874,214 is provided with a hologram element that is disposed on the spherical surface 3 and that has the shape of a curved surface.
A hologram element having a shape of a curved surface has two kinds of powers, i. e. an optical power resulting from the shape and a power resulting from the diffraction effect of the hologram element. In reference to the drawings, these two kinds of powers of a hologram element formed on a base member having a spherical surface shape, for example, are explained. The hologram element has a power resulting from difference in interference fringe density such as the pitch of the grating structure in the hologram element as shown in FIG. 17A, and has an optical power resulting from its curved surface shape as shown in FIG. 17B. The optical power of the hologram element depending on its shape is influenced by thickness of the base member also. The power depending on the shape increases as the thickness of the base member increases.
However, in the observation optical system set forth in U.S. Pat. No. 4,874,214, since the space between the plane surface (2) and the spherical surface (3) is not filled with a medium such as glass or plastic, the optical power resulting from the curved surface shape of the hologram element is small and thus it is difficult to compensate spherical aberration and coma. Furthermore, in this observation optical system, since no optical element is disposed adjacent to the image display element, or in the path between the image surface and the plane surface (2), where compensation of distortion could be effectively made, it is difficult to compensate distortion in good condition.
The present invention has been made to solve the above-mentioned problems involved in the conventional art. An object of the present invention is to provide an observation optical system that allows a displayed image to be bright as observed, is easily assembled, is insusceptible to vibration or impact, is lightweight and compact, and allows, in addition, the displayed image to be observed upon aberrations being compensated in good condition, and to provide an apparatus using the same. Also, upon the travelling direction of light in the path being inverted, such an optical system is applicable to a photographing optical system provided with an imaging optical system which forms an object image, and is applicable to an apparatus using the same.
The observation optical system according to the present invention comprises an observation image forming member which forms an image to be viewed by an observer, and an eyepiece optical member which introduces into an exit pupil formed at the position of the eye of the observer the observation image formed by the observation image forming member. In the observation optical system, the eyepiece optical member includes, at least, a first prism member and a second prism member. The first prism at least includes a first entrance surface through which rays emergent from the observation image enter the first prism, a reflecting surface which reflects the rays inside the first prism, and the first exit surface through which the rays exit out of the first prism. These surfaces are arranged with a first prism medium between. The second prism at least includes a second entrance surface through which the rays emergent from the first prism enter the second prism and a second exit surface through which the rays exit out of the second prism. These surfaces are arranged with a second prism medium between.
Since, in this way, the space inside the eyepiece optical member is filled with glass or plastic material, the optical power depending on the surface shape of each optically operative surface is made large, to compensate aberrations such as spherical aberration and coma in good condition.
Also, the observation optical system according to the present invention is constructed so that, in addition to the above-mentioned configuration, the first prism and the second prism are joined to each other via a hologram element interposed between the first exit surface and the second entrance surface.
The hologram element used as a tilted mirror to split the path achieves diffraction efficiency of nearly 100% in performing reflection by diffraction, and thus can provide bright view of the displayed image without loss of amount of light. Also, since the image display element-side prism and the eye-side prism are joined via a hologram element interposed between, to be an integral member, the assembly process can be free from possible inconsistency of optical axes and complicated works for prism setting, which otherwise would be induced by the air space. As a result, an observation optical system that is easily assembled and is insusceptible to vibration or impact can be achieved.
Also, since the hologram element is applied to the first prism and the second prism as interposed between, it is already shielded from dust. Therefore, without an additional dust shield member, this structure can prevent dust from being visible as an enlarged image and prevent the hologram element from swelling by absorption of water from outside and thus from changing its characteristic regarding the peak wavelength for diffraction.
Furthermore, the observation optical system according to the present invention is constructed so that, in addition to the above-mentioned configuration, the reflecting surface of the first prism is shaped as a concave curved surface to give a positive power for rays reflected therefrom, that the first entrance surface of the first prism is shaped as a curved surface to give a power for rays transmitted therethrough, and that the second exit surface of the second prism is shaped as a curved surface to give a power for rays transmitted therethrough.
Also, in the observation optical system according to the present invention, it is preferred that the first prism medium and the second prism medium are made of the same material.
Also, in the observation optical system according to the present invention, it is preferred that the first exit surface of the first prism and the second entrance surface of the second prism are substantially congruently shaped. Here, xe2x80x9csubstantially congruently shapedxe2x80x9d is intended to mean that difference in shape between the surfaces in the range of manufacture error is allowable.
Also, in the observation optical system according to the present invention, it is preferred that each of the first exit surface of the first prism and the second entrance surface of the second prism is shaped as a curved surface.
Whereby, distortion is compensated using the power of the hologram element determined by the surface shape of the first exit surface and the second entrance surface, and the rotationally symmetric component and the rotationally asymmetric component of chromatic aberration of magnification are compensated using the power of the hologram element generated by reflecting diffraction.
Also, in the observation optical system according to the present invention, it is preferred that each of the first exit surface of the first prism and the second entrance surface of the second prism is shaped as a rotationally symmetric spherical surface.
If the hologram element surface is designed to be spherical and is produced via application of liquid-state photopolymer etc, as a hologram element medium, onto a prism surface by spraying, application with uniform thickness can be easily achieved upon the spraying position being adjusted to coincide with the center of the curvature of the spherical surface.
The reason is given as follows. In the case of a rotationally asymmetric surface or a rotationally symmetric aspherical surface, the distance from a spraying position to the prism surface varies point by point on the surface and thus the sprayed photopolymer cannot have uniform density as applied. Whereas, in the case of a spherical surface, the spraying position of the photopolymer can be adjusted, as discussed above, to be equidistant from the prism surface.
It is noted that if the hologram element directs its concave surface to the exit pupil side, it is desirable that the photopolymer is applied to the first exit surface of the first prism, while, if the hologram element directs its convex surface toward the exit pupil side, it is desirable that the photopolymer is applied to the second entrance surface of the second prism.
Also, in the observation optical system according to the present invention, it is preferred that a ghost light removing member is provided for optically non-operative faces of the first prism and the second prism so as to prevent ghost light from being introduced to the eye of the observer, the optically non-operative faces being defined as faces of the first prism and the second prism other than optically operative faces used to transmit or reflect rays.
Where the first entrance surface of the first prism is defined as a top surface, it is effective to provide the ghost light removing member on a bottom surface and side surfaces of the eyepiece optical member. Furthermore, a region outside the effective diameter for rays on the first entrance surface, a region outside the effective diameter for rays on the reflecting surface of the first prism, and a region outside the effective diameter for rays on the second exit surface of the second prism are included in the optically non-operative faces. Application of the ghost light removing member to these regions is effective.
Also, in the observation optical system according to the present invention, it is preferred that the first entrance surface of the first prism is shaped as a rotationally asymmetric curved surface.
In this configuration, since a transmitting surface (the first entrance surface of the first prism) is disposed in front of an image forming member such as an image display element, distortion can be compensated in good condition. Although the surface in front of the image forming member such as an image display element may be shaped as a rotationally symmetric surface, it is much desirable to use a free curved surface, if optically operative faces are arranged to be decentered for the purpose of reducing the size of the observation optical system, to compensate decentered aberrations caused by the decentered arrangement.
Also, in the observation optical system according to the present invention, it is preferred that the rotationally asymmetric curved surface of the first entrance surface of the first prism is constructed of a free curved surface that defines only one plane of symmetry, and that the only one plane of symmetry coincides with a plane (Y-Z plane) in which the optical axis is folded.
Also, in the observation optical system according to the present invention, it is preferred that the hologram element is constructed and arranged to compensate both of the rotationally symmetric component and the rotationally asymmetric component of chromatic aberration of magnification by reflecting diffraction.
Use of a reflection-type hologram element for compensation of the rotationally symmetric component and the rotationally asymmetric component of the chromatic aberration of magnification can achieve high contrast.
Also, in the observation optical system according to the present invention, it is important that the following condition (1) is satisfied:
50xc2x0 less than xcex8 less than 80xc2x0xe2x80x83xe2x80x83(1)
where xcex8 is an angle formed between a tangent to the hologram element surface at an intersection with an axial chief ray and a visual axis, the axial chief ray being defined as a ray travelling between the center of the pupil surface and the center of the image surface (see FIG. 18).
A tilt angle of the hologram element surface deviating from 45xc2x0 allows the entire thickness of the observation optical system to be reduced, to achieve a compact and lightweight apparatus.
The deviation of the tilt angle of the hologram element surface from 45xc2x0 generates decentered aberrations. According to the present invention, free curved surfaces are arranged on a surface from which light from the observation image forming member enters the prism (i. e. the first entrance surface of the first prism), a surface which reflects diffracted light from the hologram element (i. e. the reflecting surface of the first prism), and a surface in front of the eye (i. e. the second exit surface of the second prism), respectively, so as to compensate these decentered aberrations. In addition, the base surface of the hologram element is spherically shaped so as to compensate coma and curvature of field in good condition.
The tilt angle of the hologram element surface in reference to the visual axis is expressed by xcex8. If the hologram element surface is shaped as a curved surface as in the present invention, xcex8 is defined between the tangent to the hologram element surface at the intersection with the axial chief ray and the visual axis, as shown in FIG. 18. In this case, it is important that Condition (1) is satisfied.
If a value of xcex8 is below the lower limit of Condition (1), the tilt angle of the tilted mirror becomes so small that the eyepiece optical member becomes thick and accordingly the observation optical system becomes large and heavy. On the other hand, if a value of xcex8 exceeds the upper limit of Condition (1), the amount of decentering of the eyepiece optical member becomes so large that compensation of decentered aberrations becomes difficult and accordingly observation of a high-contrast image with well-compensated distortion becomes difficult.
It is much desirable that the following condition (2) is satisfied:
60xc2x0 less than xcex8 less than 70xc2x0xe2x80x83xe2x80x83(2)
The upper and lower limits of Condition (2) are based on the same consideration as in Condition (1).
Also, in the observation optical system according to the present invention, it is preferred that the second exit surface of the second prism is shaped as a rotationally asymmetric curved surface that has an action of compensating at least one of those rotationally asymmetric aberrations including a rotationally asymmetric coma and a rotationally asymmetric astigmatism, which are generated at the eyepiece optical member.
Also, in the observation optical system according to the present invention, it is preferred that the rotationally asymmetric curved surface of the second exit surface of the second prism is constructed of a free curved surface defining only one plane of symmetry and that the plane of symmetry coincides with a plane (Y-Z plane) in which an optical axis is folded.
Also, according to the present invention, it is desirable that surfaces included in the first prism and the second prism are shaped as rotationally asymmetric surfaces such as free curved surfaces so as to achieve an optical system with good quality regarding compensation of rotationally asymmetric distortion and telecentricity. However, these surfaces may be shaped as rotationally symmetric surfaces such as spherical surfaces, aspherical surfaces, and anamorphic surfaces.
In the observation optical system according to the present invention, bundles of rays from the observation image formed by the observation image forming member enter the first prism as transmitted through the first entrance surface. The bundles of rays entering the first prism is incident on the volume hologram at a first incident angle, which is within the range of angular selectivity, to be reflected therefrom by diffraction, and is then reflected at the reflecting surface. The reflected bundles of rays are again incident on the volume hologram surface at a second incident angle. This time, since the second incident angle is out of the range of the angular selectivity, diffraction efficiency is extremely low and thus the bundles of rays substantially pass through the first exit surface, to enter the second prism as transmitted through the second entrance surface.
The bundles of rays entering the second prism exit therefrom as passing through the second exit surface, to be introduced to the eye of the observer.
As discussed above, according to the present invention, it is not necessary to provide a half mirror for splitting the path or to provide an air space. Therefore, an observation optical system that allows a displayed image to be bright as observed with small loss of amount of light, is easily assembled, is insusceptible to vibration or impact, is lightweight and compact, and allows, in addition, a displayed image to be observed upon aberrations being compensated in good condition, and an apparatus using the same can be achieved.
Also, the observation optical system according to the present invention may further include an optical member, such as a prism, a plane parallel glass plate and a positive or negative lens, disposed between the first entrance surface of the first prism and the observation image forming member.
Also, the observation optical system according to the present invention may further include an optical member, such as a prism, a plane parallel glass plate and a positive or negative lens, disposed between the second exit surface of the second prism and the exit pupil.
It is noted that these features of the optical system according to the present invention are applicable not only to the observation system but also to a photographing system.
A photographing optical system according to the present invention comprises an image pickup element disposed on an image surface for photographing an image of an object, an aperture stop disposed on a pupil surface for regulating brightness of a beam of rays emergent from the object, and an imaging optical member disposed between the image surface and the pupil surface for introducing the image of the object to the image surface. The imaging optical member includes, at least, a second prism member and a first prism member. The second prism at least includes a third entrance surface through which rays emergent from the object and passing through the aperture stop enter the second prism and a third exit surface through which the rays exit out of the second prism. These surfaces are arranged with a second prism medium between. The first prism at least includes a fourth entrance surface through which the rays emergent from the second prism enter the first prism, a reflecting surface which reflects the rays inside the first prism, and a fourth exit surface through which the rays exit out of the first prism. These surfaces are arranged with a first prism medium between. The second prism and the first prism are configured to be joined to one another via a hologram element interposed between the third exit surface and the fourth entrance surface. Furthermore, the reflecting surface of the first prism is shaped as a concave curved surface to give a positive power for rays reflected therefrom, the fourth exit surface of the first prism is shaped as a curved surface to give a power for rays transmitted therethrough, and the third entrance surface of the second prism is shaped as a curved surface to give a power for rays transmitted therethrough.
In other words, if the observation image forming member, the exit pupil and the eyepiece optical member of the observation optical system according to the present invention are replaced by the image pickup element, the aperture stop and the imaging optical system, respectively, the photographing optical system according to the present invention is configured.
It is preferred that the photographing optical system also has features similar to the observation optical system, such as the above-described numerical conditions.
Also, the observation optical system according to the present invention may be configured so that a mirror coating is applied to the reflecting surface of the first prism.
Also, the reflecting surface of the first prism may be configured as a total reflection surface, which reflects bundles of rays that are incident thereon at angles greater than the critical angle and which transmits bundles of rays that are incident thereon at angles not greater than the critical angle. In addition, an optical member that transmits light may be provided on the reflecting surface side of the first prism.
This configuration allows an observer to perform see-through observation. The observer can carry on wearing a head- or face-mount type image display apparatus using the observation optical system of the present invention without sacrificing normal observation of view outside. In short, the observer is not bothered to take off and on the apparatus during use.
This configuration is applicable to image superposition mode where an image from the image display element and an image from outside can be simultaneously viewed as overlapped images.
It is noted that the reflecting surface of the first prism may be constructed of a half mirror, to realize see-through observation.
Also, an image display element, a main frame in which any one of the above-mentioned observation optical system of the present invention is arranged as an eyepiece optical system, a support member which supports the main frame on the head of the observer so as to hold the exit pupil of the observation optical system at the position of the eye of the observer, and a speaker member which provides a sound for an ear of the observer can be combined into a head-mount type image display apparatus.
Such a head-mount type image display apparatus may be configured so that the main frame is provided with an observation optical system for a right eye and an observation optical system for a left eye, and that the speaker member has a speaker member for a right ear and a speaker member for a left ear.
Also, in the head-mount type image display apparatus, the speaker member may be constructed of an earphone.
In the optical system of the present invention, unless at least one of reflecting surfaces is decentered from an axial chief ray, the path of the axial chief ray incident on reflecting surfaces coincides with the path of the axial chief ray reflected therefrom and thus the axial chief ray is interrupted in the optical system, where the axial chief ray is defined as a ray travelling from the center of the object point, via the center of the pupil in the case of observation optical system or of the aperture stop in the case of the photographing optical system, through the center of the image surface, as traced in the reverse direction in the case of the observation optical system or in the forward direction in the case of the photographing optical system. As a result, a beam of rays with its central portion being interrupted is used for image formation and thus the image becomes dark at its center or the image formation is completely failed at the center. Therefore, prisms applied to the present invention are decentered prisms.
Also, in the case where a reflecting surface having a power is decentered from the axial chief ray, it is desirable that at least one of surfaces included in the prism members used in the present invention is shaped as a rotationally asymmetric surface. It is particularly preferred that at least one reflecting surface of the prism members is shaped as a rotationally asymmetric surface in view of compensation of aberrations.
In order to fold a path of rays upon repeatedly using a common region for the path, an optical system should have decentered arrangement. However, if the optical system is configured as a decentered optical system for folding the path, decentered aberrations such as a rotationally asymmetric distortion and a rotationally asymmetric curvature of field are generated. In order to compensate such decentered aberrations, rotationally asymmetric surfaces are used as mentioned above.
By the similar reason, it is desirable that the power surface of the hologram element used in the present invention also is a rotationally asymmetric surface.
The first exit surface of the first prism and the second entrance surface of the second prism, which are joined to each other via the hologram element between, may be shaped as, other than the curved or rotationally symmetric spherical surface as described above, any one of an aspherical surface, an anamorphic surface, a toric surface, a surface that defines only one plane of symmetry, and a plane-symmetric free curved surface.
Also, a rotationally asymmetric surface used in the present invention may be configured as any one of an anamorphic surface, a toric surface, and a free curved surface that defines only one plane of symmetry. Specifically, the surface is preferably configured as a free curved surface that defines only one plane of symmetry.
According to the present invention, the axial chief ray is defined, in the case of the observation optical system, as a ray travelling from the center of the exit pupil through the center of the observation image forming member as traced in the reverse direction, or, in the case of the photographing optical system, as a ray travelling from the center of the aperture stop through the center of the image pickup element as traced in the forward direction. The optical axis, which is defined by the straight line portion of the axial chief ray from the center of the exit pupil or of the aperture stop to the point of intersection with the second exit surface or with the third entrance surface of the second prism, is defined as Z axis. The axis that intersects Z axis at right angles and that lies in a plane of decentering for each surface constituting the second prism is defined as Y axis. The axis that intersects Z axis and Y axis at right angles is defined as X axis. The center of the exit pupil or of the aperture stop is determined as the origin of the coordinate system for the observation optical system or the photographing optical system of the present invention. Also, according to the present invention, surface arrangement numbers are assigned in order from the exit pupil through the observation image forming member to conform to the reverse ray tracing or in order from the aperture stop through the image pickup element to conform to the forward ray tracing. The direction of the axial chief ray from the exit pupil toward the observation image forming member or from the aperture stop toward the image pickup element is defined as a positive direction of Z axis. A direction of Y axis that is toward the observation image forming member or the image pickup element is defined as a positive direction of Y axis. A direction of X axis which forms a right hand system along with Y axis and Z axis is defined as a positive direction of X axis.
Here, the free curved surface used in the present invention is defined by the following equation (3) where Z axis appearing therein is the axis of the free curved surface:                     Z        =                                            cr              2                        /                          {                              1                +                                                      1                    -                                                                  (                                                  1                          +                          k                                                )                                            ⁢                                              c                        2                                            ⁢                                              r                        2                                                                                                        }                                +                                    ∑                              j                =                2                            66                        ⁢                                          c                j                            ⁢                              X                m                            ⁢                              Y                n                                                                        (        3        )            
The first term of Equation (3) expresses the spherical component. The second term of Equation (3) expresses the free curve component. In the term of the spherical component, c represents a curvature at the vertex, k represents a conic constant, and r={square root over (X2+Y2)}.
The term of the free curve component is expanded as shown in the following equation (4):                                                                                           ∑                                      j                    =                    2                                    66                                ⁢                                                      C                    j                                    ⁢                                      X                    m                                    ⁢                                      Y                    n                                                              =                            ⁢                                                                    C                    2                                    ⁢                  X                                +                                                      C                    3                                    ⁢                  Y                                +                                                      C                    4                                    ⁢                                      X                    2                                                  +                                                      C                    5                                    ⁢                  XY                                +                                                      C                    6                                    ⁢                                      Y                    2                                                  +                                                      C                    7                                    ⁢                                      X                    3                                                  +                                                                                                      ⁢                                                                    C                    8                                    ⁢                                      X                    2                                    ⁢                  Y                                +                                                      C                    9                                    ⁢                                      XY                    2                                                  +                                                      C                    10                                    ⁢                                      Y                    3                                                  +                                                      C                    11                                    ⁢                                      X                    4                                                  +                                                      C                    12                                    ⁢                                      X                    3                                    ⁢                  Y                                +                                                                                                      ⁢                                                                    C                    13                                    ⁢                                      X                    2                                    ⁢                                      Y                    2                                                  +                                                      C                    14                                    ⁢                                      XY                    3                                                  +                                                      C                    15                                    ⁢                                      Y                    4                                                  +                                                      C                    16                                    ⁢                                      X                    5                                                  +                                                      C                    17                                    ⁢                                      X                    4                                    ⁢                  Y                                +                                                                                                      ⁢                                                                    C                    18                                    ⁢                                      X                    3                                    ⁢                                      Y                    2                                                  +                                                      C                    19                                    ⁢                                      X                    2                                    ⁢                                      Y                    3                                                  +                                                      C                    20                                    ⁢                                      XY                    4                                                  +                                                      C                    21                                    ⁢                                      Y                    5                                                  +                                                      C                    22                                    ⁢                                      X                    6                                                  +                                                                                                      ⁢                                                                    C                    23                                    ⁢                                      X                    5                                    ⁢                  Y                                +                                                      C                    24                                    ⁢                                      X                    4                                    ⁢                                      Y                    2                                                  +                                                      C                    25                                    ⁢                                      X                    3                                    ⁢                                      Y                    3                                                  +                                                      C                    26                                    ⁢                                      X                    2                                    ⁢                                      Y                    4                                                  +                                                                                                      ⁢                                                                    C                    27                                    ⁢                                      XY                    5                                                  +                                                      C                    28                                    ⁢                                      Y                    6                                                  +                                                      C                    29                                    ⁢                                      X                    7                                                  +                                                      C                    30                                    ⁢                                      X                    6                                    ⁢                  Y                                +                                                      C                    31                                    ⁢                                      X                    5                                    ⁢                                      Y                    2                                                  +                                                                                                      ⁢                                                                    C                    32                                    ⁢                                      X                    4                                    ⁢                                      Y                    3                                                  +                                                      C                    33                                    ⁢                                      X                    3                                    ⁢                                      Y                    4                                                  +                                                      C                    34                                    ⁢                                      X                    2                                    ⁢                                      Y                    5                                                  +                                                      C                    35                                    ⁢                                      XY                    6                                                  +                                                      C                    36                                    ⁢                                      Y                    7                                                                                                          (        4        )            
where Cj (j is integer equal to or greater than 2) is a coefficient.
In general, a free curved surface as expressed above does not have a plane of symmetry along X-Z plane or along Y-Z plane. However, according to the present invention, upon all terms with odd-numbered powers of X being nullified, the free curved surface can define only one plane of symmetry that is parallel to Y-Z plane. Such a free curved surface is obtained, for example, by setting values of the coefficients C2, C5, C7, C9, C12, C14, C16, C18, C20, C23, C25, C27, C29, C31, C33, C35 . . . of the terms in Equation (4) at zero.
Alternatively, upon all terms with odd-numbered powers of Y being nullified, the free curved surface can define only one plane of symmetry that is parallel to X-Z plane. Such a free curved surface is obtained, for example, by setting values of the coefficients C3, C5, C8, C10, C12, C14, C17, C19, C21, C23, C25, C27, C30, C32, C34, C36 . . . of the terms in Equation (4) at zero.
Also, a free curved surface that defines one of the above-mentioned planes of symmetry is arranged so that its plane of symmetry corresponds to the decentering direction of the optical system. That is, a free curved surface defining a plane of symmetry parallel to Y-Z plane is combined with an optical system having decentering direction along Y axis, and a free curved surface defining a plane of symmetry parallel to X-Z plane is combined with an optical system having decentering direction along X axis, to effectively compensate rotationally asymmetric aberrations caused by decentering and to improve facility for fabrication.
Equation (3) is presented as one example that can define a free curved surface. The present invention is characteristic in compensating rotationally asymmetric aberrations resulting from decentering and improving facility for fabrication by using a rotationally asymmetric surface that defines only one plane of symmetry. Even if the free curved surface of the present invention is defined by any different expression other than Equation (3), it still has a similar effect, as a matter of course.
According to the present invention, a reflecting surface included in the prism member can be shaped as a plane-symmetric free curved surface defining only one plane of symmetry.
Configuration of an anamorphic surface is defined by the following equation (5). The normal to the optical surface at the origin of the surface shape is defined as the axis of the anamorphic surface.
Z=(Cxxc2x7X2+Cyxc2x7Y2)/[1+{1xe2x88x92(1+Kx)Cx2xc2x7X2xe2x88x92(1+Ky)Cy2xc2x7Y2}1/2]+xcexa3Rn{(1xe2x88x92Pn)X2+(1+Pn)Y2}(n+1)xe2x80x83xe2x80x83(5)
Here, if it is assumed that n is from 1 to 4 (polynomial of degree 4), for example, Equation (5) is expanded as the following expression (6):
Z=(Cxxc2x7X2+Cyxc2x7Y2)/[1+{1xe2x88x92(1+Kx)Cx2xc2x7X2xe2x88x92(1+Ky)Cy2xc2x7Y2}1/2]
+R1{(1xe2x88x92P1)X2+(1+P1)Y2}2 
+R2{(1xe2x88x92P2)X2+(1+P2)Y2}3 
+R3{(1xe2x88x92P3)X2+(1+P3)Y2}4 
+R4{(1xe2x88x92P4)X2+(1+P4)Y2}5xe2x80x83xe2x80x83(6)
where Z is an amount of deviation from a plane tangent to the origin of the surface shape, Cx is a curvature in X-axis direction, Cy is a curvature in Y-axis direction, Kx is a conical coefficient in X-axis direction, Ky is a conical coefficient in Y-axis direction, Rn is a rotationally symmetric component of a spherical surface term, and Pn is a rotationally asymmetric component of an aspherical surface term. A radius of curvature Rx in X-axis direction and a radius of curvature Ry in Y-axis direction are correlated with the curvatures Cx, and Cy, respectively, as follows:
Rx=1/Cx, Ry=1/Cy.
Regarding the toric surface, there are two kinds; i. e. X toric surface and Y toric surface, which are expressed by the following equations (7), (8), respectively. The normal to the optical surface at the origin of the surface shape is defined as the axis of the toric surface.
X toric surface is defined as follows:
F(X)=Cxxc2x7X2/[1+{1xe2x88x92(1+K)Cx2xc2x7X2}1/2]+AX4+BX6+CX8+DX10 . . . Z=F(X)+(1/2)Cy{Y2+Z2xe2x88x92F(X)2}xe2x80x83xe2x80x83(7)
Y toric surface is defined as follows;
F(Y)=Cyxc2x7Y2/[1+{1xe2x88x92(1+K)Cy2xc2x7Y2}1/2]+AY4+BY6+CY8+DY10 . . . Z=F(Y)+(1/2)Cx{X2+Z2xe2x88x92F(Y)2}xe2x80x83xe2x80x83(8)
where Z is an amount of deviation from a plane tangent to the origin of the surface shape, Cx is a curvature in X-axis direction, Cy is a curvature in Y-axis direction, K is a conical coefficient, and A, B, C, and D are aspherical coefficients. A radius of curvature Rx in X-axis direction and a radius of curvature Ry in Y-axis direction are correlated with the curvatures Cx, and Cy, respectively, as follows:
Rx=1/Cx, Ry=1/Cy.
Regarding the hologram element, there are two types; i. e. a relief hologram and a volume hologram. The relief hologram has the property of low selectivity regarding incident angle and low selectivity regarding wavelength. Thus, such a type of hologram diffracts rays with a particular wavelength incident thereon at a particular angle and images them as desired diffraction order rays, while diffracting, at a low diffraction efficiency, other rays with different wavelengths incident thereon at different angles and imaging them as undesired order rays. In contrast, the volume hologram has the property of high selectivity with respect to incident angle and high selectivity with respect to wavelength. Thus, such a type of hologram exclusively diffracts rays with a particular wavelength incident thereon at a particular angle, while transmitting the remaining rays as zero order rays so that undesired order rays should hardly be imaged.
Therefore, if a reflection-type volume hologram is used as the hologram element of the present invention, image blur because of undesired order rays is obviated, and thus a clear image can be provided for observation.
The volume hologram used as a hologram element (HOE) in the present invention is defined as follows. FIG. 19 is a view to show the principle of defining HOE according to the present invention.
Ray tracing for a ray with wavelength A incident on and emergent from any point P on the HOE surface is given by the following equation (9), which uses the optical path difference function (Do defined for a reference wavelength xcexo=HWL on the HOE surface:
ndQdxc2x7N=niQixc2x7N+m(xcex/xcex0)∇"PHgr"0xc2x7Nxe2x80x83xe2x80x83(9)
where N is a vector of the normal to the HOE surface, ni (nd) is a refractive index on the incident side (emergent side), Qi (Qd) is a vector of incidence (emergence), and m=HOR is a diffraction order of emergent light.
If the HOE is fabricated (defined) by two point light sources with the reference wavelength xcex0, specifically by interference between object rays emanating from the point P1=(HY1, HY2, HY3) and reference rays emanating from the point P2=(HX2, HY2, HZ2) as shown in FIG. 19, the following equation is satisfied:
"PHgr"0="PHgr"02P=n2xc2x7s2xc2x7r2xe2x88x92n1xc2x7s1xc2x7r1
where r1 (r2) is a distance ( greater than 0) from the point P1 (P2) to a predetermined coordinate point (i.e. the origin) O on the HOE, n1 (n2) is a refractive index of the point P1 (P2)-side medium by which the HOE was arranged during fabrication (definition), s1=HV1, and s2=HV2 are signs to take into consideration the travelling direction of light. In the case where the light source is a divergent light source (real point light source), the sign is set to be REA=+1, while in the case where the light source is a convergent light source (virtual point light source), the sign is set to be VIR=xe2x88x921. It is noted that in defining a HOE in lens data, the refractive index n1 (n2) of the medium in which the HOE was arranged during fabrication is the refractive index of the medium that is adjacent to the HOE on the side of the point P1 (P2).
In general cases, reference rays and object rays used to fabricate a HOE are not limited to spherical waves. In these cases, the optical path difference function "PHgr"0 of HOE can be defined by the following equation (10) in which an additional phase term "PHgr"0Poly (optical path difference function for the reference wavelength xcex0) expressed by polynomial terms is added:
"PHgr"0="PHgr"02P+"PHgr"0Polyxe2x80x83xe2x80x83(10)
The polynomial "PHgr"0Poly is given by:                               Φ          0          Poly                =                ⁢                              ∑            j                    ⁢                                    H              j                        ·                          x              m                        ·                          y              n                                                              =                ⁢                                            H              1                        ⁢            x                    +                                    H              2                        ⁢            y                    +                                    H              3                        ⁢                          x              2                                +                                    H              4                        ⁢            xy                    +                                    H              5                        ⁢                          y              2                                +                                    H              6                        ⁢                          x              3                                +                                                ⁢                                            H              7                        ⁢                          x              2                        ⁢            y                    +                                    H              8                        ⁢                          xy                              2                ⁢                                  xe2x80x83                                                              +                                    H              9                        ⁢                          y              3                                +          …                    
and can be defined, in general, by:
j={(m+n)2+m+3n}/2
where Hj is the coefficient of each term.
Furthermore, for convenience in optical designing, the optical path difference function "PHgr"0 may be expressed only by the additional term as follows:
"PHgr"0="PHgr"0Poly
whereby the HOE can be defined. For example, if the two point light sources P1 and P2 coincide, the component "PHgr"02P of the optical path difference function "PHgr"0 derived from interference becomes zero. This condition corresponds to the case where the optical path difference function is expressed only by the additional terms (polynomial expression).
The above descriptions regarding HOE are made in reference to a local coordinate system determined by the HOE origin.
An example of the parameter set to define the HOE is shown below:
Now, descriptions will be made of the principle of reflecting diffraction and transmission caused at the surface of the volume hologram used in the present invention. A result of a simulation, which was performed regarding the diffraction efficiency for P-polarized component based on the theory of Kogelnic, is presented. FIG. 18 shows the conditions under which the calculation of the diffraction efficiency was made. As light sources for R, G, B bands, LED light sources having center wavelengths of 630 nm, 520 nm, and 470 nm, respectively, are employed. Each of the LCDs is combined with a narrow-band filter so that its bandwidth is limited substantially within xc2x17 nm from the center wavelength. As an example, the inventor presents the calculation result of diffraction efficiency at the volume hologram surface for the axial chief ray of G band, which is obtained based on the assumption that the reference refractive index is 1.5 and the refracting diffraction angle is 0.05. The diffraction efficiency in the case where the incident angle of the axial chief ray is 45.1xc2x0 and the reflecting diffraction angle of 45.2xc2x0 is shown in FIGS. 20, 21. FIG. 20 is a graph in which the diffraction efficiency for the axial chief ray with the wavelength of 520 nm is plotted against the incident angle. FIG. 21 is a graph in which the diffraction efficiency for the axial chief ray forming the incident angle of 45.1xc2x0 is plotted against the wavelength.
As shown in FIG. 20, for the axial chief ray with the wavelength of 520 nm, the diffraction efficiency of substantially 100% is obtained in the vicinity of the incident angle of xc2x145.1xc2x0. Also, as shown in FIG. 21, the reflecting diffraction efficiency is good within the wavelength range of 520 nmxc2x17 nm. It is noted that the design is made so that the axial chief ray is again incident on the volume hologram surface at the incident mangle of 24.6xc2x0 this time, after being reflected therefrom by diffraction and reflected from the reflecting surface of the first prism. As shown in FIG. 20, when the axial chief ray having the wavelength of 520 nm is incident on the volume hologram surface region with the above-described properties regarding the incident angle and the diffraction angle, at the incident angle of xc2x124.6xc2x0, which is out of the range of the angular selectivity of the volume hologram element within which high diffraction efficiency is assured, the diffraction efficiency becomes as low as 0%, and thus the axial chief ray passes through the hologram element.
Also, in the later-described embodiments, the incident angle and the reflecting diffraction angle of the axial chief ray on the volume hologram surface are 45.1xc2x0 and 45.2xc2x0, respectively.
This and other objects as well as features and advantages of the present invention will become apparent from the following detailed description of the preferred embodiments when taken in conjunction with the accompanying drawings.